Theory and Experiment on Formation-Containment Control of Multiple Multirotor Unmanned Aerial Vehicle Systems

Formation-containment control problems for multiple multirotor unmanned aerial vehicle (UAV) systems with directed topologies are studied, where the states of leaders form desired formation and the states of followers converge to the convex hull spanned by those of the leaders. First, formation-containment protocols are constructed based on the neighboring information of UAVs. Then, sufficient conditions for multi-UAV systems to achieve formation-containment are presented. An explicit expression to describe the relationship among the states of followers, the time-varying formation for the leaders and the formation reference is derived. It is shown that the states of followers not only converge to the convex hull formed by those of leaders but also keep certain formation specified by the convex combination of the formation for the leaders. Moreover, an approach to determine the gain matrices of the formation-containment protocol is proposed by solving an algebraic Riccati equation. Finally, a formation-containment platform with five quadrotor UAVs is introduced, and both the simulation and experimental results are presented to demonstrate the effectiveness of the obtained results. Note to Practitioners-This paper addresses the problem of formation-containment control for multi-UAV systems over directed topologies. In practical applications, there may exist multiple leaders and multiple followers in a multi-UAV system. Formation-containment means that the states of leaders form the desired time-varying formation and at the same time the states of the followers converge to the convex hull spanned by those of the leaders. Formation-containment control provides a unified framework for formation control and containment control, and has potential applications in the cooperative source seeking, load transportation, and surveillance. Although formation control and containment control problems have been studied a lot, the formation-containment control problem for multi-UAV system is still open and challenging. This paper proposed a distributed formation-containment protocol for the multi-UAV system using local neighboring information. Sufficient conditions for multi-UAV systems to achieve formation-containment are presented. It is proven that the states of followers not only converge to the convex hull formed by those of leaders but also keep certain formation specified by the convex combination of the formation for the leaders. An approach to design the formation-containment protocol is given. A remarkable point for this paper is that the obtained results are demonstrated by practical experiments with five quadrotor UAVs.